A casing running tool comprising an integral elevation module and make-up/torque module. In accordance with one aspect or the invention, the tool is adapted to automatically engage a collared end of a tubular structure such as a casing string segment. The integral make-up/torque module is actuated by hydraulic control lines to exert compression force upon the outer diameter of a tubular, such as a casing string segment. This compression force is sufficient to enable torque to be applied to the tubular without slippage. In one embodiment, the make-up/torque module comprises an outer body carrying a plurality of hydraulically-actuable pistons, such that the tool is actuable from the rig floor to grasp the tubular with sufficient force that rotational force (torque) supplied via a drive motor in a top-drive rig. In accordance with another embodiment, the multifunction tool further includes an internal ball valve assembly for selectively allowing or restricting fluid flow through the tool. The elastic strength of biasing means on either end of the ball valve assembly takes into account possible over- or under hydraulic pressures which may exist within the tubulars already deployed.